Mechanical Engineering Dimensionless Numbers

Notations and units:

Re = Reynolds Number, Nu = Nusselt Number, Pr = Prandtl Number, Gr = Grashof Number, µ = Dynamic viscosity

\nu = Kinematic viscosity, L_{ch} = Diameter or Length based on the environment, C = Specific heat, \mu_{f} = Coefficient of friction, K = Thermal conductivity, h = Heat transfer coefficient, g = acceleration due to gravity, β = Coefficient of thermal expansion, T = Temperature

Units of the notations are in SI units.

1.Stanton Number = Heat transferred into fluid / Thermal capacity of the fluid 

Stanton Number = \frac{Nu}{Re \times Pr} = \frac{\mu_{f}}{2 \times (Pr)^{2/3}}

2.Schmidt Number = Momentum diffusivity or kinematic viscosity / Mass diffusivity

3.Sherwood Number = Convective mass transfer / Diffusion mass transfer

4.Lewis Number = Thermal diffusivity / Mass diffusivity

5.Peclet Number = Convective heat transfer / Conductive heat transfer

6.Reynolds Number = Inertia force / Viscous force

Reynolds Number = \frac{Velocity(V) \times L_{ch}}{\nu}

\nu = dynamic viscosity / mass density

7.Euler Number = inertia force / pressure force

8.Prandtl Number = diffusion of momentum / diffusion of heat

Prandtl Number = \frac{\mu\times C}{K}

Prandtl Number = Velocity boundary layer thickness / Thermal boundary layer thickness

9.Nusselt Number = Conduction resistance of the fluid / Convection resistance of the fluid

Nusselt Number = \frac{h\times L_{ch}}{K}

10.Grashof Number = (buoyancy force / viscous force) x Re

Grashof Number = \frac{g\beta(T_{surface}-T_{fluid})L_{ch}^{3}}{\nu^{3}}

11.Cauchy Number = inertia force / elastic force

12.Fourier Number = ability of the solid to conduct energy / ability to store energy

13.Rayleigh Number = Gr x Pr

14.Froude Number = inertia force / gravity force

15.Weber Number = inertia force / surface tension force

16.Mach Number = velocity of the stream / velocity of the sound

17.Biot Number = internal conductive resistance of the solid / convective resistance of the fluid

Biot Number = \frac{h\times L_{ch}}{K}

 

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